scholarly journals CB-Norm Estimates for Maps Between NoncommutativeLp-Spaces and Quantum Channel Theory

2015 ◽  
Vol 2016 (3) ◽  
pp. 875-925 ◽  
Author(s):  
Marius Junge ◽  
Carlos Palazuelos
Keyword(s):  
Quantum Channel ◽  
Norm Estimates ◽  
Channel Theory

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

Mapping quantum channel decoherence

2020 ◽  
Author(s):  
Daniel E. Jones ◽  
Gabriele Riccardi ◽  
Cristian Antonelli ◽  
Michael Brodsky
Keyword(s):  
Quantum Channel

scholarly journals Fundamental limitations on distillation of quantum channel resources

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bartosz Regula ◽  
Ryuji Takagi
Keyword(s):  
Lower Bounds ◽  
Quantum Channel ◽  
Quantum Communication ◽  
Fault Tolerant ◽  
State Of The Art ◽  
Quantum Systems ◽  
Noisy Channels ◽  
General Transformation ◽  
Fundamental Limitations ◽  
Strong Converse

AbstractQuantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

scholarly journals Norm estimates for Chebyshev polynomials, I

2021 ◽  
pp. 105561
Author(s):  
Klaus Schiefermayr ◽  
Maxim Zinchenko
Keyword(s):  
Chebyshev Polynomials ◽  
Norm Estimates
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